A person with osteoarthritis of the knee (a common condition in middle-aged and elderly individuals) plans to have a knee replacement. Assume he has a quasi-linear utility function ( U ( )) over wage w and his health H. That is, U (w ,H) = w + 10 4 ln H. Suppose with an artificial knee, the person can enjoy 20 additional healthy days annually during the next 10 years, during which he can earn a wage of $150/day. The annual interest rate is 2 percent.

a. Calculate the annual increase in wages based on the information in the problem.

b. Calculate the Present Value of the annual increase in wages, starting at year 0 (0 -9).

c. Calculate the Present Value of the annual gain in utility ( w = annual wage increase), ln is the natural log ( you can get ln50, etc. by going into google and type ln 50 and it will give you the answer if you do not have a calculator with a ln function.

Year	1	2	3	4	5	6	7	8	9	10
Health Capital	50	49	48	46	43	39	34	28	21	12